Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#14268636 | C2 | semidirect |
| 2. #20299169 | C2 | semidirect |
| 4. #20298844 | C2 | semidirect |
| 5. #20298827 | C2 | semidirect |
| 6. #20298636 | C2 | semidirect |
| 7. #20298608 | C2 | semidirect |
| 8. #20298604 | C2 | semidirect |
| 9. C2×#131×C113 | C2 | semidirect |
| 20. #16813601 | C22 | semidirect |
| 25. #16813556 | C22 | semidirect |
| 26. #16813554 | C22 | semidirect |
| 27. #16813547 | C22 | semidirect |
| 32. C2×M16×C113 | C22 | semidirect |
| 34. C22×C8×C113 | C22 | semidirect |
| 67. C2×C8×C113 | D4 | semidirect |
| 121. C113 | #3057 | semidirect |
| 123. C2×#131 | D113 | semidirect |
| 139. C2×M16 | C2×D113 | semidirect |
| 141. C22×C8 | C2×D113 | semidirect |
| 179. C2×C8 | C22⋊D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268636 | 2 |
| #20299169 | 2 |
| #20299162 | 2 |
| #20298844 | 2 |
| #20298827 | 2 |
| #20298636 | 2 |
| #20298608 | 2 |
| #20298604 | 2 |
| C2×#131×C113 | 2 |
| #3057 | 113 |